Let \(Y_1\)  and \(Y_2\)  be two compact oriented 4-manifolds. If a closed manifold \(Y\)  is obtained by gluing along the whole boundaries of \(Y_1\)  and \(Y_2\)  via an orientation reversing diffeomorphism, then the signature of \(Y\)  is equal to sum of the signatures of \(Y_1\)  and \(Y_2.\)  This is Novikov additivity [1]}. On the other hand it is also possible to glue manifolds \(Y_1\)  and \(Y_2\)  along common submanifold \(X_0\)  in their boundary where \(X_0\)  may itself have boundary. In this case, the resulting manifold \(Y\)  is a 4-manifold with boundary and its signature is not the sum of the signatures of \(Y_1\)  and \(Y_2\) , the defect in this argument is a Maslov ternary index[2]}.
